When carrying out a complicated groove cutting in a cylindrical workpiece, using an end mill at a machining center or the like, the machining operation is effected by controlling a cylindrical axis (Z) and a rotary axis (C), and for such a machining, a cylindrical interpolation system is widely used to facilitate the preparation of a machining program.
FIG. 9 illustrates the cylindrical interpolation system, wherein a cylindrical surface is developed as an assumed plane 2a and an assumed orthogonal coordinate system is established based on the Z axis and an assumed linear axis Cy. This coordinate system is identical to a usual plane coordinate system, and a path of a tool 1 with reference to the orthogonal coordinate system is derived by a program. Since the shape to be machined is programmed with reference to a cylindrical coordinate system, it is converted into the assumed orthogonal coordinate system. After the interpolation for the Z and Cy axes is effected with reference to the orthogonal coordinate system, the amount of movement of the Cy axis is converted back (from the orthogonal coordinate system to the cylindrical coordinate system) into an amount of rotation of the axis of rotation (C axis) 6 of a workpiece 2, to thereby control the C axis. Such a cylindrical interpolation system permits an easy preparation of a program for a complicated groove cutting.
Nevertheless, in the prior art cylindrical interpolation system, the tool cutting surface is not always at right angles to the cylindrical surface. FIG. 10 shows the relationship between a tool and a workpiece during groove cutting according to a prior art cylindrical interpolation, in which a tool axis 1a is controlled so that it is at right angles to the cylindrical surface of the workpiece 2, and therefore, the tool cutting surface 5 and a line 3 perpendicular to the cylindrical surface of the workpiece 2 form a constant angle therebetween. As a result, a hatched portion 4 is cut unnecessarily, and thus a desired machining cannot be carried out.